A snow plough has a 3.2m blade set at an angle of 30 degrees How wide a path will the snow plough clear

1.6m

Step-by-step explanation:

The length of the blade is 3.2m

The angle which the blade makes is 30°

Assuming the path of the blade and the length it covers is a right-angled triangle,

The length of the blade is the hypothenus while the path at which it clears is the opposite of the triangle.

See attached document for better illustration.

Using SOHCAHTOA,

Sinθ = opposite / hypothenus

opposite = x

hypothenus = 3.2

θ = 30°

Sin30 = x / 3.2

X = 3.2sin30

X = 3.2 × 0.5

X = 1.6m

The path which the snow plough clears is 1.6m

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

45

step-by-step explanation: